Chapter 7, Problem 377RE

In the following exercises, determine the values for which the rational expression is undefined.

377. $\frac{5a+3}{3a-2}$

To determine

The value for which rational function is undefined.

Answer to Problem 377RE

$a=\frac{2}{3}$.

Explanation of Solution

Given information:

The given rational function is $R\left(x\right)=\frac{\left(5a+3\right)}{\left(3a-2\right)}$.

Calculation:

The given rational function will become undefined if denominator of the rational function $R\left(x\right)=\frac{\left(5a+3\right)}{\left(3a-2\right)}$ becomes zero.

$\begin{array}{l}\Rightarrow \left(3a-2\right)=0\\ \Rightarrow a=\frac{2}{3}\end{array}$

$\text{At }a=\left(\frac{2}{3}\right)$

$\begin{array}{l}R\left(x\right)=\frac{5\left(\frac{2}{3}\right)+3}{3\left(\frac{2}{3}\right)-2}\\ R\left(x\right)=\frac{\left(\frac{10}{3}\right)+3}{2-2}\\ R\left(x\right)=\frac{\left(\frac{10}{3}\right)+3}{0}\\ R\left(x\right)=\infty \end{array}$

Rational function is undefined, when $a=\frac{2}{3}$.